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Derivatives — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSDerivatives2 Marks
Question
Differentiate the following functions with respect to x:$\frac{1}{\text{ax}^2+\text{bx}+\text{c}}$
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Answer

$\frac{\text{d}}{\text{dx}}\Big(\frac{1}{\text{ax}^2+\text{bx}+\text{c}}\Big)$$=\frac{(\text{ax}^2+\text{bx}+\text{c})\frac{\text{d}}{\text{dx}}(1)-1\frac{\text{d}}{\text{dx}}(\text{ax}^2+\text{bx}+\text{c})}{(\text{ax}^2+\text{bx}+\text{c})^2}$
$=\frac{-(\text{2ax}+\text{b})}{(\text{ax}^2+\text{bx}+\text{c})^2}$
$\therefore\frac{\text{d}}{\text{dx}}\frac{1}{\text{ax}^2+\text{bx}+\text{c}}=\frac{-(\text{2ax}+\text{b})}{(\text{ax}^2+\text{bx}+\text{c})^2}$

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